Scattering cross-section definition

In Eq. (7.21) the normalization to the scattering cross-section r2 leads to the definition of absolute intensity in electron units which is common in materials science. If omitted [90,91], the fundamental definition based on scattering length density is obtained (cf. Sect. 7.10.1). 

This definition leads to an electron density measured in electrons per nm3 (cf. Sect. 7.10.1). If we are aiming at a treatment in terms of scattering cross-section we define /o = Zre, instead. 

Let us derive a relation between the deflection angle and the scattering cross-section. From the definition of the cross-section, Eq. (4.6), specialized to classical elastic two-body scattering with one scattering center, we get... 

The time-independent probability for the occurrence of a particular collision process is represented by the corresponding scattering cross section. It characterises the scattering process and is well defined in most scattering experiments. There are some situations when a time-dependent probability must be considered and the normal definition of a scattering cross section is not applicable. 

From these definitions, it is clear that bCO and blnC° can be changed merely by modifying the relative concentration of the various isotopes. This fact is of great practical importance in neutron experiments (isotopic substitution). The coherent and incoherent scattering cross-section are defined by... 

In Chapter 6, we defined the centres which scatter neutrons or photons as being (respectively) nuclei or electrons. In this chapter, the set of all the centres belonging to a monomer will be considered as a unique scattering centre. This more economical definition is justified by the fact that, in the interval (0, qm ) where we study the behaviour of scattering cross-sections, the length q x is always large as compared to atomic distances. Let rai be the position vector of the centre of mass of monomer i. Then, suppose... 

This is the definition of the total scattering cross-section as(u). When we are concerned with the chemical reaction... 

In view of (8.28) and from the definition of Gs(r,f) in Section 8.1.2, we find the incoherent component of the double differential scattering cross section to be... 

In this appendix, we summarise the formulae required in the calculation of neutron scattering cross-sections, give an example of such a calculation and conclude with tables of the necessary coefficients. Firstly, we remind you of the definition of the cross-section obtained in sect. 2.2.4. 

In the next section (Sec. 2), we will develop the theory of the BCRLM. We discuss the solution of the coupled-channel equations in both natural collision coordinates " and hyperspherical coordinates. " Both coordinate systems are widely used to treat collinear reactive scattering processes. We will discuss the projection " of the hyperspherical equations on coordinate surfaces appropriate for applying scattering boundary conditions and review the definition of integral and differential scattering cross sections in this model. 

In these experiments, the significant quantities are the scattering cross sections given by the ratio of the constant intensities and which by definition are respectively proportional to the transition rate and to the incident photon flux. Hence... 

The gamma function F is used in the definition of the Coulomb phase shift.) There are three potential observables for elastic scattering. The first is the differential (elastic) scattering cross section,... 

More experimental work on antiparticle/particle-atom collisions had to await the technical development of antiparticle beams of higher intensity and velocity definition at lower particle velocities. Since the late sixties, a large number of such experiments were performed for c /c impact on gaseous targets. Elastic- and total-scattering cross sections were measured as well as the cross section for positronium formation. A recent review of this work was given by Charlton and Laricchia [2.12]. Since 1980, it has become possible to measure cross sections for ionization and excitation in antiparticle-atom collisions. It is these results that are the primary subject of the present paper. However, we also include... 

A formal definition of these two scattering cross sections is as follows ... 

All of the effective collision cross sections introduced above can, in principle, be evaluated from a knowledge of the intermolecular pair potential by means of equation (4.17) and the definition of the collision operator (4.5). This process would then make it possible to predict the transport properties of dilute gases from first principles. However, such a procedure would require that it is possible to evaluate the inelastic differential scattering cross section ajj or an equivalent to it which enters (4.5). Until very recently this could only be accomplished for dilute monatomic gases. There were two reasons for this first, only for such systems are accurate intermolecular potentials available (Aziz 1984 Maitland et al. 1987 van der Avoird 1992) second, only for such systems was the... 

In the early days of chemical dynamics (the 1960 s) the study of elastic scattering was an important project, both experimentally and theoretically, for developing the tools to be used to study more interesting processes, e.g., elastic scattering of the rare gas atoms. Y.T.Lee s (1986 Nobel Prize with M. Polanyi and D. Herschbach) measurements of the differential scattering cross sections allowed the definitive determination of the intermolecular potential energy function V(r) of essentially all the rare gas atoms with each other... 

The total scattering cross-section is by definition independent of 0 and 0 and we have assumed independent of position for simplicity. Second, there is a gain from power scattered into direction 0, 0. Ignoring contributions from leaky rays, the total contribution is from bound rays, whose range of 0 values satisfies Eq. (2-6a). Thus the power gained, dPg, is found by integrating Eq. (5-64) over the cross-section... 

The extinction and scattering cross-sections can be expressed in terms of the expansion coefficients amn, mn, fmn and Qmn- Denoting by Sc the circumscribing sphere of outward unit normal vector Br and radius R, and using the definition of the extinction cross-section (cf. (1.82) and (1.83) with leo = 1), yields... 

The scatterer (aperture) is finite in extent. Moreover, owing to the loss in the metal, fields decay in the film away from the aperture hence, /g, /aa — /af and /c are finite quantities. The definition of the scattering cross section is analogous to the antenna case. However, in the definition of the absorption cross section, we replace /a with /aa — /af. In the case of the antenna, the term was stated to be directly proportional to the radiation intensity in the forward direction. For the aperture, a Green s function analysis similar to the antenna case indicates that the contribution to Iq from the surface SI — S2 — S3 is proportional to the radiation intensity in the forward direction. Similarly, the contribution from the surface S4 — S5 — S6 is proportional to the radiation intensity in the backward direction. Thus, /c is a linear combination of the radiation intensity in the forward and backward directions. 

---